Nowadays, the MIMO technique is widely known in the art of wireless communication, and is based on the use of multiple antennas at both the transmitter and receiver of a telecommunication system in order to improve communication capacity or/and performance.
One well known transmission technique used in MIMO systems is the so-called spatial multiplexing and is based on the transmission of independent and separately encoded data signals from each of the multiple transmit antennas of a wireless communication system. In that way, the space dimension is reused (multiplexed) more than one time, leading to a data flow increase. Spatial multiplexing is a very efficient technique for increasing channel capacity at higher signal-to-noise ratios (SNR).
However, a main spatial multiplexing MIMO problematic lies on the signal detection process. In particular, the processing resources used in detectors of spatial multiplexing MIMO systems, are not always adequate for detecting the signal received by the receiver of such systems. One well known detector considered for signal detection in spatial multiplexing MIMO communication systems is the optimal but infeasible Maximum Likelihood (ML) detector.
FIG. 1 illustrates a MIMO system which comprises a transmitter Tx including multiple transmit antennas and a receiver Rx including multiple receive antennas. The multiple antennas of the transmitter Tx send multiple data signals (streams) through a channel represented by a complex matrix H taking account of all the paths between the transmit antennas and the receive antennas. Afterwards, the receiver Rx receives the data signals by the multiple antennas and decodes those vectors, thus providing the transmit vector estimate belonging to the original information. In particular, a MIMO system can be modeled as follows:r=Hs+n  (1)where r and s represent a receive and a transmit signal vector respectively, while H and n represent the channel matrix and a noise vector respectively.
It can be seen on the equation above, that the detection of the transmitted signal s with the classical linear detectors would require the (pseudo-)inversion of matrix H which, even in the case of OFDM, would be full rank because of the MIMO architecture.
Generally speaking, in the more recent receivers, this computation of the transmitted signal is solved by means of a so-called QR Decomposition (QRD) which accuracy is critical so as to ensure good detection performance of the receiver.
As known by the skilled man, a QRD (also called a QR factorization) is based on a decomposition of channel matrix H in two distinctive matrices, i.e. a first unitary matrix Q and a second—upper triangular—matrix R as illustrated in FIG. 2. The significant advantage of QRD is that it provides a way of making the receive vector entries iteratively independent, thus reducing the complexity of the QRD-based detector compared to the ML joint detector. Specifically, because of the unitary nature of matrix Q (which means that QHQ=I), the Hs term in equation (1) is multiplied by QH and thus simultaneously reads Rs and QHy which is possibly solved in a system resolving-like way, since R is triangular. Thus, the ML equation from (1) can be re-arranged and thus can be iteratively solved. The transmit signals of the MIMO system can then be detected from the received signal by the receiver and decoded by any known technique so as to regenerate the original symbols s.
There are several methods for computing the QRD, such as the Gram-Schmidt process, the Householder transformations, or the Givens rotations.
Firstly, in the Gram-Schmidt process, QRD consists of two steps, namely orthogonalization and normalization steps. In the orthogonalization step, a normal vector of the matrix Q that is already normalized in the normalization step is obtained and the remaining columns of Q are orthogonalized to the obtained column. Note that the matrix Q is initiated to H. Therefore, the corresponding row of the matrix R is obtained from Q.
Secondly, the Householder reflection (or Householder transformation) is a transformation that is used to obtain the upper triangular matrix R from which the matrix Q can be obtained if required. The idea behind this technique is to obtain the matrix R using a reflection matrix. This reflection matrix, also known as Householder matrix, is used to cancel all the elements of a vector except its first element which is assigned the norm of the vector. Therefore, the columns of the matrix H are treated iteratively to obtain the R matrix. Thirdly, QRD can also be computed with a series of so-called Givens rotations. Each rotation zeros an element in the subdiagonal of the matrix H, so that a triangular shape R is obtained. The concatenation of all the Givens rotations forms the orthogonal Q matrix.
Other techniques are also known which do not need further development.
However, in all those prior art methods, the full QRD processing is needed at every detection processing of a transmit vector and lies on a periodical estimation of a channel matrix H. Especially in the case of multi-carrier MIMO systems, the overall computational complexity of QRD is significantly increased since the full QRD for each channel estimation requires much more processing power than the conventional detectors may offer.
It would be desirable to provide an alternative technique which is more suitable for processors used in the mobile equipments, and which processors cannot, generally speaking, support the huge amount of processing resources required by the known prior art techniques.